Mpemba effect

The Mpemba effect is a process in which hot water can freeze faster than cold water. The phenomenon is temperature-dependent. There is disagreement about the parameters required to produce the effect and about its theoretical basis.[1][2]

The Mpemba effect is named after Erasto Bartholomeo Mpemba (b.1950) who discovered it in 1963. There were preceding ancient accounts of similar phenomena, but lacking sufficient detail to attempt verification.

Definition

The phenomenon, when taken to mean "hot water freezes faster than cold", is difficult to reproduce or confirm because this statement is ill-defined.[3] Monwhea Jeng proposes as a more precise wording:

There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner.[4]

However, even with this definition it is not clear whether "freezing" refers to the point at which water forms a visible surface layer of ice; the point at which the entire volume of water becomes a solid block of ice; or when the water reaches 0 °C (32 °F).[3] A quantity of water can be at 0 °C (32 °F) and not be ice; after enough heat has been removed to reach 0 °C (32 °F) more heat must be removed before the water changes to solid state (ice), so water can be liquid or solid at 0 °C (32 °F).

With the above definition there are simple ways in which the effect might be observed. For example, if the hotter temperature melts the frost on a cooling surface and thus increases the thermal conductivity between the cooling surface and the water container.[3] On the other hand, there may be many circumstances in which the effect is not observed.[3]

Observations

Historical context

Various effects of heat on the freezing of water were described by ancient scientists such as Aristotle: "The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner. Hence many people, when they want to cool water quickly, begin by putting it in the sun. So the inhabitants of Pontus when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their reeds that it may freeze the quicker, for they use the ice like lead to fix the reeds."[5] Aristotle's explanation involved antiperistasis, "the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality."

Early modern scientists such as Francis Bacon noted that, "slightly tepid water freezes more easily than that which is utterly cold."[6] In the original Latin, "aqua parum tepida facilius conglacietur quam omnino frigida."

René Descartes wrote in his Discourse on the Method, "One can see by experience that water that has been kept on a fire for a long time freezes faster than other, the reason being that those of its particles that are least able to stop bending evaporate while the water is being heated."[7] This relates to Descartes' vortex theory.

The Scottish scientist Joseph Black investigated a special case of this phenomenon comparing previously-boiled with unboiled water;[8] the previously-boiled water froze more quickly. Evaporation was controlled for. He discussed the influence of stirring on the results of the experiment, noting that stirring the unboiled water led to it freezing at the same time as the previously-boiled water, and also noted that stirring the very-cold unboiled water led to immediate freezing. Joseph Black then discussed Fahrenheit's description of supercooling of water (although the term supercooling had not then been coined), arguing, in modern terms, that the previously-boiled water could not be as readily supercooled.

Mpemba's observation

The effect is named after TanzanianErasto Mpemba. He described it in 1963 in Form 3 of Magamba Secondary School, Tanganyika, when freezing ice cream mix that was hot in cookery classes and noticing that it froze before the cold mix. He later became a student at Mkwawa Secondary (formerly High) School in Iringa. The headmaster invited Dr. Denis G. Osborne from the University College in Dar es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question, "If you take two similar containers with equal volumes of water, one at 35 °C (95 °F) and the other at 100 °C (212 °F), and put them into a freezer, the one that started at 100 °C (212 °F) freezes first. Why?", only to be ridiculed by his classmates and teacher. After initial consternation, Osborne experimented on the issue back at his workplace and confirmed Mpemba's finding. They published the results together in 1969, while Mpemba was studying at the College of African Wildlife Management.[9]

Modern context

Mpemba and Osborne describe placing 70 ml (2.5 imp fl oz; 2.4 US fl oz) samples of water in 100 ml (3.5 imp fl oz; 3.4 US fl oz) beakers in the ice box of a domestic refrigerator on a sheet of polystyrene foam. They showed the time for freezing to start was longest with an initial temperature of 25 °C (77 °F) and that it was much less at around 90 °C (194 °F). They ruled out loss of liquid volume by evaporation as a significant factor and the effect of dissolved air. In their setup most heat loss was found to be from the liquid surface.[9]

David Auerbach describes an effect that he observed in samples in glass beakers placed into a liquid cooling bath. In all cases the water supercooled, reaching a temperature of typically −6 to −18 °C (21 to 0 °F) before spontaneously freezing. Considerable random variation was observed in the time required for spontaneous freezing to start and in some cases this resulted in the water which started off hotter (partially) freezing first.[10]

James Brownridge, a radiation safety officer at the State University of New York, has said that he believes that supercooling is involved.[11] Several molecular dynamics simulations have also supported that changes in hydrogen bonding during supercooling takes a major role in the process.[12][13]

In 2016, Burridge and Linden defined the criterion as the time to reach 0 °C (32 °F), carried out experiments and reviewed published work to date. They noted that the large difference originally claimed had not been replicated, and that studies showing a small effect could be influenced by variations in the positioning of thermometers. They say, "We conclude, somewhat sadly, that there is no evidence to support meaningful observations of the Mpemba effect".[1]

However, in 2017, two research groups independently and simultaneously found theoretical evidence of the Mpemba effect and also predicted a new "inverse" Mpemba effect in which heating a cooled, far-from-equilibrium system takes less time than another system that is initially closer to equilibrium. Lu and Raz[14] yield a general criterion based on Markovian statistical mechanics, predicting the appearance of the inverse Mpemba effect in the Ising model and diffusion dynamics. Lasanta and co-workers[15] predict also the direct and inverse Mpemba effects for a granular gas in a far-from-equilibrium initial state. In this last work, it is suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity distribution function that significantly deviates from the Maxwell-Boltzmann distribution.

Suggested explanations

The following explanations have been proposed:

Evaporation: The evaporation of the warmer water reduces the mass of the water to be frozen.[16] Evaporation is endothermic, meaning that the water mass is cooled by vapor carrying away the heat, but this alone probably does not account for the entirety of the effect.[4]

Convection: Accelerating heat transfers. Reduction of water density below 4 °C (39 °F) tends to suppress the convection currents that cool the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling. Higher convection in the warmer water may also spread ice crystals around faster.[17]

Frost: Has insulating effects. The lower temperature water will tend to freeze from the top, reducing further heat loss by radiation and air convection, while the warmer water will tend to freeze from the bottom and sides because of water convection. This is disputed as there are experiments that account for this factor.[4]

Thermal conductivity: The container of hotter liquid may melt through a layer of frost that is acting as an insulator under the container (frost is an insulator, as mentioned above), allowing the container to come into direct contact with a much colder lower layer that the frost formed on (ice, refrigeration coils, etc.) The container now rests on a much colder surface (or one better at removing heat, such as refrigeration coils) than the originally colder water, and so cools far faster from this point on.

Dissolved gases: Cold water can contain more dissolved gases than hot water, which may somehow change the properties of the water with respect to convection currents, a proposition that has some experimental support but no theoretical explanation.[4]

Recent views

A reviewer for Physics World writes, "Even if the Mpemba effect is real — if hot water can sometimes freeze more quickly than cold — it is not clear whether the explanation would be trivial or illuminating." He pointed out that investigations of the phenomenon need to control a large number of initial parameters (including type and initial temperature of the water, dissolved gas and other impurities, and size, shape and material of the container, and temperature of the refrigerator) and need to settle on a particular method of establishing the time of freezing, all of which might affect the presence or absence of the Mpemba effect. The required vast multidimensional array of experiments might explain why the effect is not yet understood.[3]

New Scientist recommends starting the experiment with containers at 35 and 5 °C (95 and 41 °F) to maximize the effect.[19] In a related study, it was found that freezer temperature also affects the probability of observing the Mpemba phenomenon as well as container temperature.

In 2012, the Royal Society of Chemistry held a competition calling for papers offering explanations to the Mpemba effect.[20] More than 22,000 people entered and Erasto Mpemba himself announced Nikola Bregović as the winner. Bregović suggests two reasons for the effect — a colder sample gets supercooled rather than frozen, and enhanced convection in the warmer sample speeds up cooling by maintaining the heat gradient on the container walls.[21]

Tao and co-workers proposed yet another possible explanation in 2016. On the basis of results from vibrational spectroscopy and modeling with density functional theory-optimized water clusters, they suggest that the reason might lie in the vast diversity and peculiar occurrence of different hydrogen bonds. Their key argument is that the number of strong hydrogen bonds increases as temperature is elevated. The existence of the small strongly-bonded clusters facilitates in turn the nucleation of hexagonal ice when warm water is rapidly cooled down.[2]

Similar effects

Other phenomena in which large effects may be achieved faster than small effects are:

^Black, Joseph (1 January 1775). "The Supposed Effect of Boiling upon Water, in Disposing It to Freeze More Readily, Ascertained by Experiments. By Joseph Black, M. D. Professor of Chemistry at Edinburgh, in a Letter to Sir John Pringle, Bart. P. R. S.". Philosophical Transactions of the Royal Society of London. 65: 124–128. doi:10.1098/rstl.1775.0014.

The College of African Wildlife Management (CAWM) commonly known as Mweka College or just Mweka, is located near the Village of that name on the southern slopes of Mount Kilimanjaro in Tanzania, above the city of Moshi, about 14 kilometres north of its centre.

The locality also gives its name to the Mweka Trail, one of the routes on Kilimanjaro, used for the descent.

Following the independence of Tanganyika in 1961, the College of African Wildlife Management was established in 1963 by Bruce Kinloch as a pioneer institution for the training of African wildlife managers. Initial funding for Mweka was provided by the African Wildlife Leadership Foundation (now known as the African Wildlife Foundation), the U.S. Agency for International Development, and the Frankfurt Zoological Society, with facilities donated by the government of Tanganyika. Since this time, the College has been a leader in providing quality wildlife management training in Africa, and has trained over 5,000 wildlife managers from 52 countries worldwide (28 African countries and 24 other countries in the world), the majority are working in protected areas throughout sub-Saharan Africa.

The majority of the College's students come from the SADC region, although the College opens its doors to all students with an interest in African wildlife management. A good number of students also come from countries such as Western and Eastern Europe, United States, India, Sri Lanka, Japan and many other countries.

The College has led the field of wildlife management training in Africa for 42 years, receiving a number of awards and accolades including the prestigious UNEP Sasakawa Environment Prize and being declared a centre of excellence as a Wildlife Training Institute by the East African Community.The college was founded with stringent academic discipline, its qualifications being justly renowned both within Tanzania and internationally. Good staff and facilities, both academic and sporting, guaranteed a high standard of education and therefore of graduate too.

The college, in theory, serves two main purposes:

1) To prepare both local and international students for work within the national parks and reserves of Tanzania and whole Africa.

2) To prepare students for work within the safari industries (photographic & hunting) within Tanzania and whole Africa.

A counterintuitive proposition is one that does not seem likely to be true when assessed using intuition, common sense, or gut feelings.Scientifically discovered or mathematically proven objective truths are often called counterintuitive when intuition, emotions, and other cognitive processes outside of deductive rationality interpret them to be wrong. However, the subjective nature of intuition limits the objectivity of what to call counterintuitive because what is counterintuitive for one may be intuitive for another. This might occur in instances where intuition changes with knowledge. For instance, many aspects of quantum mechanics or general relativity may sound counterintuitive to a layman, while they may be intuitive to a particle physicist.

Flawed intuitive understanding of a problem may lead to counterproductive behavior with undesirable outcomes. In some such cases, counterintuitive policies may then produce a more desirable outcome. This can lead to conflicts between those who hold deontological and consequentialist ethical perspectives on those issues.

Erasto Bartholomeo Mpemba (1950) is a Tanzanian scientist who discovered the eponymous Mpemba effect during his school days, a paradoxical phenomenon in which hot water freezes faster than cold water under certain conditions. In 1963, he discovered the phenomenon in the preparation of ice cream. The correctness of his observations was proven experimentally.During his studies at the College of African Wildlife Management near Moshi, he published in 1969, together with Dr. Denis G. Osborne, a paper on the phenomenon. Later he worked in the Department of Natural Resources and Tourism in the Wildlife Division. He has since retired.

Freezing is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point. In contrast, solidification is a similar process where a liquid turns into a solid, not by lowering its temperature, but by increasing the pressure that it is under. Despite this technical distinction, the two processes are very similar and the two terms are often used interchangeably.

For most substances, the melting and freezing points are the same temperature; however, certain substances possess differing solid–liquid transition temperatures. For example, agar displays a hysteresis in its melting point and freezing point. It melts at 85 °C (185 °F) and solidifies from 32 °C to 40 °C (89.6 °F to 104 °F).

An ice cube is a small piece of ice, which is rectangular as viewed from above and trapezoidal as viewed from the side. Ice cubes are products of mechanical refrigeration and are usually produced to cool beverages. They may be produced at home in a refrigerator with an ice tray or in an automated ice-making accessory. They may also be produced industrially and sold commercially.

An ice resurfacer is a vehicle or hand-pushed device used to clean and smooth the surface of a sheet of ice, usually in an ice rink. The first ice resurfacer was pioneered and developed in 1949 in the city of Paramount, California by American inventor and engineer Frank Zamboni. As such, an ice resurfacer is often referred to as a "Zamboni" regardless of brand or manufacturer.

The Leidenfrost effect is a physical phenomenon in which a liquid, close to a mass that is significantly hotter than the liquid's boiling point, produces an insulating vapor layer that keeps the liquid from boiling rapidly. Because of this 'repulsive force', a droplet hovers over the surface rather than making physical contact with the hot surface.

This is most commonly seen when cooking, when a few drops of water are sprinkled in a hot pan. If the pan's temperature is at or above the Leidenfrost point, which is approximately 193 °C (379 °F) for water, the water skitters across the pan and takes longer to evaporate than it would take if the water droplets had been sprinkled into a cooler pan. The effect is responsible for the ability of a person to quickly dip a wet finger in molten lead, or blow out a mouthful of liquid nitrogen, without injury. The latter is potentially lethal, particularly should one accidentally swallow the liquid nitrogen.The effect is named after Johann Gottlob Leidenfrost, who described it in A Tract About Some Qualities of Common Water in 1751.

This is a list of paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article. Although considered paradoxes, some of these are simply based on fallacious reasoning (falsidical), or an unintuitive solution (veridical). Informally, the term paradox is often used to describe a counter-intuitive result.

However, some of these paradoxes qualify to fit into the mainstream perception of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called antinomy, point out genuine problems in our understanding of the ideas of truth and description.

In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates, neutron-degenerate matter, and quark–gluon plasma, which only occur, respectively, in situations of extreme cold, extreme density, and extremely high energy. For a complete list of all exotic states of matter, see the list of states of matter.

Historically, the distinction is made based on qualitative differences in properties. Matter in the solid state maintains a fixed volume and shape, with component particles (atoms, molecules or ions) close together and fixed into place. Matter in the liquid state maintains a fixed volume, but has a variable shape that adapts to fit its container. Its particles are still close together but move freely. Matter in the gaseous state has both variable volume and shape, adapting both to fit its container. Its particles are neither close together nor fixed in place. Matter in the plasma state has variable volume and shape, and contains neutral atoms as well as a significant number of ions and electrons, both of which can move around freely.

The term phase is sometimes used as a synonym for state of matter, but a system can contain several immiscible phases of the same state of matter.

Water is a transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms. It is vital for all known forms of life, even though it provides no calories or organic nutrients. Its chemical formula is H2O, meaning that each of its molecules contains one oxygen and two hydrogen atoms, connected by covalent bonds. Water is the name of the liquid state of H2O at standard ambient temperature and pressure. It forms precipitation in the form of rain and aerosols in the form of fog. Clouds are formed from suspended droplets of water and ice, its solid state. When finely divided, crystalline ice may precipitate in the form of snow. The gaseous state of water is steam or water vapor. Water moves continually through the water cycle of evaporation, transpiration (evapotranspiration), condensation, precipitation, and runoff, usually reaching the sea.

Water covers 71% of the Earth's surface, mostly in seas and oceans. Small portions of water occur as groundwater (1.7%), in the glaciers and the ice caps of Antarctica and Greenland (1.7%), and in the air as vapor, clouds (formed of ice and liquid water suspended in air), and precipitation (0.001%).Water plays an important role in the world economy. Approximately 70% of the freshwater used by humans goes to agriculture. Fishing in salt and fresh water bodies is a major source of food for many parts of the world. Much of long-distance trade of commodities (such as oil and natural gas) and manufactured products is transported by boats through seas, rivers, lakes, and canals. Large quantities of water, ice, and steam are used for cooling and heating, in industry and homes. Water is an excellent solvent for a wide variety of chemical substances; as such it is widely used in industrial processes, and in cooking and washing. Water is also central to many sports and other forms of entertainment, such as swimming, pleasure boating, boat racing, surfing, sport fishing, and diving.

In chemistry a water cluster is a discrete hydrogen bonded assembly or cluster of molecules of water. These clusters have been found experimentally or predicted in silico in various forms of water; in ice, in crystal lattices and in bulk liquid water, the simplest one being the water dimer (H2O)2 . Shu et al. reported the images of water clusters of 100 micrometres. Ongoing academic research is important because the realization that water manifests itself as clusters rather than an isotropic collection may help explain many anomalous water characteristics such as its highly unusual density temperature dependence. Water clusters are also implicated in the stabilization of certain supramolecular structures. So little is understood about water clusters in bulk water that it is considered one of the unsolved problems in chemistry.

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